Help - resistance of the mesh
 User Name Stay logged in? Password
 Home Forums Rules Articles diyAudio Store Blogs Gallery Wiki Register Donations FAQ Calendar Search Today's Posts Mark Forums Read Search

 Everything Else Anything related to audio / video / electronics etc) BUT remember- we have many new forums where your thread may now fit! .... Parts, Equipment & Tools, Construction Tips, Software Tools......

 Please consider donating to help us continue to serve you. Ads on/off / Custom Title / More PMs / More album space / Advanced printing & mass image saving
Irakli
diyAudio Member

Join Date: Aug 2004
Location: washington, DC
Help - resistance of the mesh

Hi All,

What is the resistance between points A and B. All resistanses in the mesh are equal to R. The mesh size(NxN) is large.

I remember solving this problem when I was in school, but can't do it now

I also remember it has a very elegant solution.

If you know the answer, please give me a hint
Attached Images
 mesh.jpg (17.2 KB, 62 views)
__________________
My System

 17th September 2010, 04:14 AM #2 bob91343   diyAudio Member   Join Date: Mar 2010 I remember that one. You draw equipotential lines and, since they are equipotential you can connect them without changing anything. Once you have done that the entire thing becomes trivial. Since the array is symmetrical, you short the same way on both sides. Actually the one I recall was a cube of resistors where you measure across the diagonal. This one is similar. So fold the whole thing top over to the bottom, hinging on the A-B line. That leaves resistors only below and all are now R/2 except the ones on the hinge line. Last edited by bob91343; 17th September 2010 at 04:17 AM.
 17th September 2010, 04:22 AM #3 zigzagflux   diyAudio Member     Join Date: Oct 2006 Location: Charlotte, NC I'll guess at 0.6R
Irakli
diyAudio Member

Join Date: Aug 2004
Location: washington, DC
Quote:
 Originally Posted by bob91343 I remember that one. You draw equipotential lines and, since they are equipotential you can connect them without changing anything. Once you have done that the entire thing becomes trivial. Since the array is symmetrical, you short the same way on both sides. Actually the one I recall was a cube of resistors where you measure across the diagonal. This one is similar. So fold the whole thing top over to the bottom, hinging on the A-B line. That leaves resistors only below and all are now R/2 except the ones on the hinge line.

Cube is easy

with this mesh we can fold it across AB line, but this does not help much
__________________
My System

 17th September 2010, 05:46 AM #5 bob91343   diyAudio Member   Join Date: Mar 2010 I wonder if it helps that you would get the same value no matter which resistor you pick, since the array is infinite. So you can substitute for any resistor the value of the total matrix. I don't know. This isn't really an electronics problem; it's a logic or math problem.
 17th September 2010, 06:31 AM #6 wwenze   diyAudio Member   Join Date: Mar 2008
Irakli
diyAudio Member

Join Date: Aug 2004
Location: washington, DC
Quote:
 Originally Posted by wwenze Build it?
Thanks, always nice to have experimental conformation.
__________________
My System

 23rd September 2010, 01:05 AM #8 Irakli   diyAudio Member     Join Date: Aug 2004 Location: washington, DC Searched the web intensely and what I thought an "elegant" solution seems to be a very spooky one. Idea is to pump in current in one node (point A) and pump it out from another one (point B). Total current through A->B supposed to be i/4+i/4=i/2, thus Rtot=R/2. I do not think that i/4 current will flow each direction because of symmetry. Symmetry is broken with the presence of the second node. Symmetry case would work if someone wants to measure resistance between arbitrary node and infinitely remote point. May be I am missing something. __________________ My System

 Posting Rules You may not post new threads You may not post replies You may not post attachments You may not edit your posts BB code is On Smilies are On [IMG] code is On HTML code is Off Forum Rules
 Forum Jump User Control Panel Private Messages Subscriptions Who's Online Search Forums Forums Home Site     Site Announcements     Forum Problems Amplifiers     Solid State     Pass Labs     Tubes / Valves     Chip Amps     Class D     Power Supplies     Headphone Systems Source & Line     Analogue Source     Analog Line Level     Digital Source     Digital Line Level     PC Based Loudspeakers     Multi-Way     Full Range     Subwoofers     Planars & Exotics Live Sound     PA Systems     Instruments and Amps Design & Build     Parts     Equipment & Tools     Construction Tips     Software Tools General Interest     Car Audio     diyAudio.com Articles     Music     Everything Else Member Areas     Introductions     The Lounge     Clubs & Events     In Memoriam The Moving Image Commercial Sector     Swap Meet     Group Buys     The diyAudio Store     Vendor Forums         Vendor's Bazaar         Sonic Craft         Apex Jr         Audio Sector         Acoustic Fun         Chipamp         DIY HiFi Supply         Elekit         Elektor         Mains Cables R Us         Parts Connexion         Planet 10 hifi         Quanghao Audio Design         Siliconray Online Electronics Store         Tubelab     Manufacturers         AKSA         Audio Poutine         Musicaltech         Aussie Amplifiers         CSS         exaDevices         Feastrex         GedLee         Head 'n' HiFi - Walter         Heatsink USA         miniDSP         SITO Audio         Twin Audio         Twisted Pear         Wild Burro Audio

 Similar Threads Thread Thread Starter Forum Replies Last Post andyjevans Tubes / Valves 38 30th October 2017 08:01 PM sportoghese Tubes / Valves 6 2nd July 2010 08:19 AM wicked1 Tubes / Valves 7 19th May 2008 03:37 PM AndrewJ Parts 3 25th May 2003 08:26 AM Mohan Varkey Tubes / Valves 1 30th March 2003 08:08 PM

 New To Site? Need Help?

All times are GMT. The time now is 08:53 AM.

 Home - Contact Us - Advertise - Rules - diyAudio Store - Sponsors - Privacy Statement - Terms of Service - Top - Opt-out policy

Search Engine Optimisation provided by DragonByte SEO (Pro) - vBulletin Mods & Addons Copyright © 2018 DragonByte Technologies Ltd.
Resources saved on this page: MySQL 15.00%
vBulletin Optimisation provided by vB Optimise (Pro) - vBulletin Mods & Addons Copyright © 2018 DragonByte Technologies Ltd.